We present a hybrid framework for convex mixed-integer nonlinear programming. In one extreme case, the method becomes the branch-and-bound approach, where a nonlinear optimization problem is solved in each node of the enumeration tree, and in the other extreme it reduces to the polyhedral outer approximation algorithm, which alternates between the solution of a nonlinear optimization problem and a mixed-integer linear program.

Numerical results are presented, using an open source software implementation available on http://www.coin-or.org.

This work results from an on-going research collaboration between IBM and CMU.